The European commission is on Wednesday expected to back diluted proposals pressing for 40% of company directors to be female by 2020 after failing to clear the 27-strong commission three weeks ago in the face of opposition by member governments orchestrated by Britain.

Brussels will press ahead with efforts to propel many more women on to boards. Rather than imposing a 40% quota on pain of penalties, the latest draft encourages companies to aim for that level of representation but leaves national governments to decide whether to enforce the rules by inflicting sanctions.

The campaign for quotas has been spearheaded by Viviane Reding of Luxembourg, the justice and fundamental rights commissioner, who senior officials suspect has ambitions of securing a top EU post after 2014.

Her plan will again be attacked by the government. In a speech, Maria Miller, the culture secretary and women and equalities minister, will accuse Reding of "patronising women" while arguing that the UK's voluntary code has resulted in key successes.

Miller will say: "The way to do this is not through special treatment or regulation like the European commission's quotas idea, which patronises women and undermines the business case. It is about removing the barriers to achieving [women's] goals, so that women are supported all the way from the shopfloor to the boardroom. We are making real progress in driving transparency and equality in our workplaces and will continue to do even more."

Reding's previous proposal divided Brussels, with the 27 commissioners unable to agree on a piece of draft legislation for the very first ti me under their president, José Manuel Barroso. It instantly ran into strong hostility from national governments, with Britain's effort to stop the imposition of female quotas gaining support across northern Europe.

Despite the perception that the Reding draft had the support of feminists, several of the most prominent women in the commission, including foreign policy chief Lady Ashton, voted against. Many leading businesswomen have also come out against Reding's plan, including Burberry chief executive officer Angela Ahrendts – who in the new year will be one of only two female bosses left in the FTSE-100 and who branded obligatory quotas as dangerous.

The government believes it is already making progress after Lord Davies' report into women in the boardroom last year recommended that FTSE-100 companies filled 25% of board roles with women by 2015. At the time of its publication, female directors held 12.5% of board positions, but research by the Public Boards Forum shows the current figure is 17.3%. Davies is now considering extending the proposals to FTSE-250 companies, which have even lower levels of female participation.

It is not clear whether Reding's watered-down legislation will win support from member governments, but it is likely to be supported in the European parliament, where MEPs have to adopt it before it can become law.

Despite the setbacks and questioning of Reding's motives, some senior EU officials argue that her policies may end up achieving good results for all the wrong reasons. They say that even if the quotas proposal has been diluted it will still set a benchmark against which the countries of the EU will be measured, with peer pressure applied by more "progressive" member states.

Miller will also use her speech to announce a £2m scheme aimed at boosting childcare and getting more women into work.

From April 2013 people who want to set up a nursery or a childminding business will be able to access grants of up to £500 to help cover legal and insurance costs, health and safety training and equipment.

She will say: "Good quality, affordable and reliable childcare is the key to even more women being able to work. More childcare options mean more women can take up jobs, help support their families and realise their own career ambitions."